One fundamental issue with existing reputation systems, particularly those implemented in open and decentralized environments, is whitewashing attacks by opportunistic participants. If identities are cheap, it is beneficial for a rational provider to simply defect when selling services to its clients, leave the system to avoid punishment and then rejoin with a new identity. Current work usually assumes the existence of an effective identity management scheme to avoid the problem, without proposing concrete solutions to directly prevent this unwanted behavior. This article presents and analyzes an incentive mechanism to effectively motivate honesty of rationally opportunistic providers in the aforementioned scenario, by eliminating incentives of providers to change their identities. The main idea is to give each provider an identity premium, with which the provider may sell services at higher prices depending on the duration of its presence in the system. Our price-based incentive mechanism, implemented with the use of a reputation-based provider selection protocol and a reverse auction scheme, is shown to significantly reduce the impact of malicious and strategic ratings, while still allowing explicit competition among the providers. It is proven that if the temporary cheating gain by a provider is bounded and small and given a trust model with a reasonable low error bound in identifying malicious ratings, our approach can effectively eliminate irrationally malicious providers and enforce honest behavior of rationally opportunistic ones, even when cheap identities are available. We suggest an identity premium function that helps such honesty to be sustained given a certain cost of identities and analyze incentives of participants in accepting the proposed premium. Related implementation issues in different application scenarios are also discussed.